One-dimensional QCD at finite density and its 't Hooft-Veneziano limit

TL;DR

This paper provides an exact solution to one-dimensional lattice gauge theories at finite temperature and chemical potential for various gauge groups and flavors, analyzing phase transitions and limits relevant to QCD.

Contribution

It offers a comprehensive analysis of exact solutions in 1D QCD models across different limits, including large N and 't Hooft-Veneziano, with detailed phase structure insights.

Findings

Uncovered Roberge-Weiss phase transition at large N_f

Calculated partition functions, free energy, and correlation functions for all N and N_f

Compared limits with real QCD models like U(3) and SU(3)

Abstract

An exact solution of one-dimensional lattice gauge theory at finite temperature and non-zero chemical potential is reviewed for the gauge groups $G=Z(N),U(N),SU(N)$ for all values of $N$ and the number of fermion flavors $N_f$. Calculated are the partition function, free energy, the Polyakov loop expectation values, baryon density, quark condensate, meson and baryon correlation functions. Detailed analysis of the exact solutions is done for $N=2,3$ with one and two fermion flavors. In the large $N_f$ limit we uncover the Roberge-Weiss phase transition and discuss its remnants at finite $N_f$. In the case of $N_f$ degenerate flavors we also calculate 1) the large $N$ limit, 2) the large $N_f$ limit and 3) the 't Hooft-Veneziano limit of all models. The critical behavior of the models in these limits is studied and the phase structure is described in details. A comparison of all limits with $U(3)$ and $SU(3)$ QCD is also performed. In order to achieve these results we explore several representations of the partition function of one-dimensional QCD obtained and described in the text.